An experiment was performed to study the effect of three different types of strings (factor A)...

 

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An experiment was performed to study the effect of three different types of strings (factor A) -Polyester (A1), Synthetic gut (A2), and Multifilament (A3) and three different tennis racket types (factor B) - Wilson pro staff 97 (B1), Yonex EZONE 98 (B2), and Babolat Pure (B3) - - on the serve speed (y in km/hour) of tennis players. The experiment is designed with objective of achieving the highest serve speed. Three professional players (factor C) were involved in this experiment, and two replicates were run. The observed serving data are shown in the following Table Q3. (a) (b) Player Bottle Туре C1 A1 A2 A3 A1 A2 A3 A1 A2 A3 C2 C3 B1 103.5 122.1 126 144 135.6 148.8 122.4 129 125.1 Replicate 1 B2 124.2 131.4 127.8 156.6 154.5 155.1 118.2 135.9 145.8 B3 174 164.4 170.1 186.3 187.5 180.9 154.2 149.7 145.5 Table Q3 B1 100.8 105.6 110.4 132 133.2 131.7 109.5 121.2 116.4 Replicate 2 B2 125.7 127.8 131.1 141 139.5 142.5 122.4 122.4 134.4 B3 156.9 145.5 167.4 176.4 186 191.4 134.7 137.7 147 Demonstrate the factorial design that can be used in this experiment and explain the reasons. (4 marks) Based on the data (Table Q3), please show all the codes to construct the ANOVA table in R for the chosen design in Question 3(a). Further interpret your conclusion on the model, A, B, C and their interactions. (10 marks) (c) The interaction plot is shown in Figure Q3(c). Please analyse the figure and draw a conclusion. (4 marks) 180 160 Serve Speed 140 120 1 2 Player Figure Q3(c) 3 Racket Type 3 2 1 An experiment was performed to study the effect of three different types of strings (factor A) -Polyester (A1), Synthetic gut (A2), and Multifilament (A3) and three different tennis racket types (factor B) - Wilson pro staff 97 (B1), Yonex EZONE 98 (B2), and Babolat Pure (B3) - - on the serve speed (y in km/hour) of tennis players. The experiment is designed with objective of achieving the highest serve speed. Three professional players (factor C) were involved in this experiment, and two replicates were run. The observed serving data are shown in the following Table Q3. (a) (b) Player Bottle Туре C1 A1 A2 A3 A1 A2 A3 A1 A2 A3 C2 C3 B1 103.5 122.1 126 144 135.6 148.8 122.4 129 125.1 Replicate 1 B2 124.2 131.4 127.8 156.6 154.5 155.1 118.2 135.9 145.8 B3 174 164.4 170.1 186.3 187.5 180.9 154.2 149.7 145.5 Table Q3 B1 100.8 105.6 110.4 132 133.2 131.7 109.5 121.2 116.4 Replicate 2 B2 125.7 127.8 131.1 141 139.5 142.5 122.4 122.4 134.4 B3 156.9 145.5 167.4 176.4 186 191.4 134.7 137.7 147 Demonstrate the factorial design that can be used in this experiment and explain the reasons. (4 marks) Based on the data (Table Q3), please show all the codes to construct the ANOVA table in R for the chosen design in Question 3(a). Further interpret your conclusion on the model, A, B, C and their interactions. (10 marks) (c) The interaction plot is shown in Figure Q3(c). Please analyse the figure and draw a conclusion. (4 marks) 180 160 Serve Speed 140 120 1 2 Player Figure Q3(c) 3 Racket Type 3 2 1